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TECHNICAL EFFICIENCY OF SMALLHOLDER IRISH POTATO

PRODUCTION IN NYABIHU DISTRICT, RWANDA

BY

GATEMBEREZI MUZUNGU PAUL

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE

REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN

AGRICULTURAL& APPLIED ECONOMICS

DEPARTMENT OF AGRICULTURAL ECONOMICS

FACULTY OF AGRICULTURE

COLLEGE OF AGRICULTURE AND VETERINARY SCIENCES

UNIVERSITY OF NAIROBI, KENYA

JULY, 2011

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DECLARATION

I declare that this is my original work and has not been submitted in any to any other

University for the award of a degree.

Sign ------------------------------------------------------------------------------------

Paul Muzungu Gatemberezi

(Candidate)

This thesis has been submitted to Board of Postgraduate Studies for approval with the

consent of the following University supervisors:

Signature: ----------------------- ----------------------Date----------------

Dr Richard Mbiti Mulwa

Department of Agricultural Economics

University of Nairobi

Signature: -------------------------------- -----------Date------------------

Dr Jonathan Nzuma

Department of Agricultural Economics

University of Nairobi

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DEDICATION

This thesis is dedicated to my lovely wife Antoinette Kankindi for her unconditional

encouragement and our children:

Nshuti Jonathan, Ingabire Joyce, Ineza Deborat, Manzi David and Rebecca Hirwa

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ACKNOWLEDGEMENT I would like to thank God for seeing me throughout the course of my entire study and

stay in Kenya and South Africa. I begin this acknowledgement with thanks and gratitude

to my supervisors, Dr Mulwa Richard and Dr Nzuma Jonathan for their friendly and useful

advice, guidance and corrections that helped me to complete this work.

I give my sincere gratitude to the Southern Junior Researchers awards program (IDRC

Canada) for providing me with a scholarship through the African Economic Research

Consortium (AERC)/Collaborative Master of Science in Agricultural and Applied

Economics (CMAAE) Programme to pursue a Master of Science degree in Agricultural

and Applied Economics at University of Nairobi- Kenya for the financial support.

Finally, I thank all the staff of the Department of Agricultural Economics ,Faculty of

Agriculture, University of Nairobi for the knowledge they imparted to me throughout

my stay at this institution. I am also grateful to Mr Karangwa Matthias who introduced

me to the STATA computer program.

To God be the Glory

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TABLE OF CONTENT

Declaration.......................................................................................................................... i

Dedication .......................................................................................................................... ii

Acknowledgement ............................................................................................................ iii

Table of content................................................................................................................ iv

List of tables...................................................................................................................... vi

List of tables..................................................................................................................... vii

List of figures.................................................................................................................. viii

List of acronyms and abbreviations ............................................................................... ix

Abstract .............................................................................................................................. x

CHAPTER I....................................................................................................................... 1

INTRODUCTION ............................................................................................................. 1

1.1 Background Information............................................................................................... 1

1.2 Potato Production in Rwanda........................................................................................ 2

1.3 Problem statement......................................................................................................... 4

1.4 Purpose and Objectives of the study............................................................................. 5

1.5 Hypotheses……………………………………………………………………….……6

1.6 Justification of the study ............................................................................................... 6

CHAPTER II ..................................................................................................................... 7

LITERATURE REVIEW ................................................................................................ 7

2.1. The Concept of Efficiency........................................................................................... 7

2.2 Approaches to measuring efficiency............................................................................. 9

2.3 Concept of Data Envelopment Analysis (DEA) ......................................................... 10

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2.4 Technical, Allocative and Economic Efficiency ........................................................ 11

2.5 Technical Efficiency: Empirical Application ............................................................. 13

CHAPTER III ................................................................................................................. 20

METHODOLOGY ......................................................................................................... 20

3.1 Analytical framework ................................................................................................. 20

3.1.1 Theoretical framework: Stochastic frontier production..........................................20

3.2 Empirical model.......................................................................................................... 23

3.3 Data needs and Source................................................................................................ 30

3.3.1 Determination of the sample size............................................................................. 30

3.3 .2 Sampling Procedure................................................................................................ 31

3.3.3 Data Preparation and Analysis................................................................................. 32

3.4 The Study Area ........................................................................................................... 32

CHAPTER IV. .................................................................................................................. 35

RESULTS AND DISCUSSIONS..................................................................................... 35

4.1. Householder Characteristics ...................................................................................... 35

4.1.1 Household size....................................................................................................... 35

4.1.2 Gender and Maritial status....................................................................................... 36

4.1.3 Education Level ....................................................................................................... 38

4.1.4 Area under Potato .................................................................................................... 39

4.1.5 Experience of growing potato.................................................................................. 40

4.1.6 Extension services.................................................................................................... 41

4.1.7 Access to credit ........................................................................................................ 42

4.2 Estimation of Technical efficient in potato production ............................................ 43

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4.2.1 Output and input variables in potato production...................................................... 43

4.2.3 Testing for the presence of inefficiency in potato production ............................... 46

4.2 .3 Production frontier and Technical efficiency estimates.......................................... 47

4.2.4 Elasticities and Return to scale ............................................................................. 51

4.3. Factors influencing Technical efficiency................................................................... 52

4.3.1 House hold size ........................................................................................................ 53

4.3.2 Education level of household................................................................................... 53

4.3.3 Gender...................................................................................................................... 54

4.3.4 Farm size.................................................................................................................. 54

4.3.5 Marital status............................................................................................................ 54

4.3.6 Experience of farmer growing potato ...................................................................... 55

4.3.7 Extension services and access to credit ................................................................. 55

CHAPTER V ................................................................................................................... 57

SUMMARY, CONCLUSIONS AND RECOMMENDATIONS ................................ 57

5.1 Summary................................................................................................................... 57

5.2 .Conclusion ................................................................................................................. 58

5.3 Recommendation ........................................................................................................ 59

5.4. Suggestions for Further Research .............................................................................. 60

REFERENCES ................................................................................................................. 61

APPENDIX....................................................................................................................... 70

2. QUESTIONNAIRE FOR POTATO PRODUCERS ................................................... 73

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LIST OF TABLES

Table 1.1 Population trend of Rwanda over time ............................................................... 1

Table 3. 1 Variables in the stochastic Cobb-Douglas production model.......................... 27

Table 3.2: Description of variables included in the Inefficiency Model and their expected

signs .................................................................................................................................. 29

Table 4.1 Farmer distribution according to gender and marital status ............................. 37

Table 4.2 Potato Farm area category ................................................................................ 40

Table 4.3 Experience of farmer growing potato ............................................................... 41

Table 4.5 Distribution of farmer to access to credit.......................................................... 42

Table 4.6 Summary descriptive statistics of output and input variables in .................. 44

Potato production (Kg, ha, man-day)................................................................................ 44

Table 4.7 Testing hypothesis on the presence of inefficiency in potato production

Nyabihu District................................................................................................................ 47

Table 4.8 Maximum likelihood estimates of the stochastic frontier production function 49

Table 4. 9 Input Elasticity............................................................................................... 51

Table 4.10 Determinants of technical inefficiency and Socio-economic Characteristics 52

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LIST OF FIGURES

Figure 1.1: Potato production trend in Rwanda................................................................ 3

Figure 2.1: Concept of Technical and Allocative Efficiencies ......................................... 12

Figure 3.1: Administrative Map of Nyabihu District........................................................ 33

Figure 4.1: Family size ..................................................................................................... 36

Figure 4.2: Education level of household head................................................................. 39

Figure 4.3: The distribution of technical efficiency.......................................................... 50

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LIST OF ACRONYMS AND ABBREVIATIONS

AE: Allocative Efficiency

AUP: Area under Potato

CIT: Central Intelligence Agency

COLS: Corrected Ordinary Least Square method

C-D: Cobb- Douglas

DEA: Data Envelopment Analysis

DMU: Decision Making Units

DRTS: Decreasing Return to Scale

DRC: Democratic Republic of Congo

EE: Economic Efficiency

FAO: Food Agriculture Organization

GDP: Gross Domestic Product

GoR: Government of Rwanda

MINAGRI: Ministry of Agriculture

MLE: Maximum Likelihood Estimate

MT: Million tones

NIS: National Institute of Statistics

OLS : Ordinary Least Square

RoR: Republic of Rwanda

SFA: Stochastic Frontier Approach

TE: Technical Efficiency

TIE: Technical Inefficiency

WFP: World Food Program

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ABSTRACT The study on technical efficiency of smallholder Potato was carried out in Nyabihu

District of Rwanda. The study estimates the technical efficiency obtained from stochastic

frontier production approach. The paper estimates the levels of technical efficiency for

150 smallholder potato farmers, and provides an empirical analysis of the determinants of

inefficiency with the aim of finding a way to increase smallholders’ potato production

and productivity. The study used of both primary and secondary data. Primary data was

obtained directly from respondents (farmers) while secondary data were obtained from

books, journals and records of Ministry of Agriculture.

Data was collected through trained enumerators using pre-tested questionnaire. The

survey was conducted during the month of April and May 2010 Data collected was

analysed using STATA and SPSS computer programs. Maximum likelihood estimates

are obtained from half – normal stochastic production model.

Results indicated that 71 percent variation in the output of Irish potato production was

attributed to technical inefficiency with a mean of 60.5 percent technical efficiency. It is

shown that area under potato, seed, and family labor and fertilizes, contribute positively

towards the improvement of efficiency. The analysis also reveals that, farming

experience, house hold size, gender, marital status, farm size, extension services are

socio-economic factors influencing the farmers’ technical efficiency. However,

education, access to credit and firm size brought negative impacts in affecting the

efficiency level of farmers. To achieve increased efficiency of production, this study

recommends government to allocate more funds in strengthening the extension services

and increasing agricultural credit services to potato growers.

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CHAPTER ONE

INTRODUCTION

1.1 Background Information

Rwanda is a small landlocked country located in Eastern and Central Africa region,

between Burundi, Uganda, Tanzania and the Democratic Republic of Congo (DRC). The

climate is moderate and characterized by temperate conditions, especially in higher

altitudes in the Northwest of the country. The topography is hilly to mountainous with

altitude ranging from 950 to 2,500 meters above sea level (CIA, 2005). The population

is estimated at 9.06 million and was growing at a rate of about 2.5% per year, a rate that

may double the 2006 population in about 28 years (Republic of Rwanda, RoR, 2006).

The population density estimated at 344 persons per square kilometer (CIA, 2005).

Rwanda has had a rapid demographic increase since 1952. Table 1.1 below shows the

trend of the population growth in Rwanda.

Table 1.1 Population trend of Rwanda over time

1952 1970 1980 1990 2002 2006 2009 2010

2,000,000 3,769,171 5,138,478 6,981,760 8,278,209 9,060000

10,117,033 10,768,777

(Source: NIS, 2007)

Agriculture is the most important sector of the Rwandan economy; It contributes 41% of

Gross Domestic Product (GDP) and employs around 90% of the Rwandan population

which lives in rural areas (NIS 2008). Agriculture is important for sustainable

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development, poverty reduction, and enhanced food security, and supplies over 90% of

the food consumed in the country while manufacturing accounts for only 13 per cent of

GDP (FAO, 2008). Indeed, promoting agriculture is imperative to achieve the

Millennium Development goal (World Bank, 2008).

1.2 Potato Production in Rwanda

Irish potato is the second most important food crop in Rwanda after Cassava (Mpyisi,

2002). It plays an important role both as a food and a cash crop in the country. Potato has

become an increasingly important sector in Rwanda in terms of potential for contributing

to food security, nutrition, employment and improvement in socio –economic status of

rural communities. According to Ministry of Agriculture potato comes as a first strategy

to reduce poverty. This crop is concentrated in the highland areas of North –Western

Rwanda, in the districts of Nyabihu, Musanze and Rubavu, where all households

cultivate potatoes and produce over 60 percent of the national production (NIS,2006).

However, Nyabihu district alone produces between 50 and 60 percent of the total annual

potato consumed in the Country (MINAGRI 2000). Irish potato is one of the most

important crops that are grown in Nyabihu District both for food security and income.

Rwanda classified potato as a priority crop for development and food security that can

serve as an example to the rest of the agriculture sector how rapid transformation can

take place (GoR, 2000). Potatoes are essentially a food security crop especially in urban

areas and as a result the annual consumption is about 125 kg per person, making potato

the country's second most important source of calorie intake after cassava. (Nyarwaya et.

al, 2002). According to Ministry of Agriculture (MINAGRI, 2006), potato production had

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almost tripled from 1986 to 2006. In fact, was 241.7 MT in 1986, and 2006 654.9 MT in

2006. The highest potato production in Rwanda comes from Nyabihu Districts, followed

by Musanze District with production of 291.5MT or 44.5 % and 178.045 MT or 27.28%

respectively. These two Districts comprise 72.3 % of national level production.

(MINAGRI, 2006).

Figure 1.2: Potato production trend in Rwanda

Source: MINAGRI, 2007

This crop has an important role as food and an important opportunity for marketing,

hence improving productivity in the Irish potato sub-sector and reducing poverty is a

major policy objective of the Rwandan government.

According to FAO( 2008), Rwanda is the sixth largest producer of potatoes in Africa

after Egypt, Malawi, South Africa, Algeria, and Morocco. (FAO, 2008).

However, given population growth rates, particularly in urban cities, potato remains

preferences consumption and high demand for domestic markets. The challenge for the

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country now is to supply food which is not keeping pace with population growth. To fill

the gap between supply and demand, Rwandan government import grains and other food.

Additionaly, 52 percent of households are food insecure or vulnerable (NIS and WFP,

2006). While several efforts were undertaken by the Government of Rwanda to increase

production food crop, Irish potato still faces a declining trend in yield. The declining of

Irish potato production is due to several factors, such as, scarcity of arable land, reduction

of soil fertility and the rapidly increasing demand for food due to a high rate of

population growth.

1.3 Problem statement

As indicated earlier, Agriculture remains the backbone of Rwanda’s economy. Potato

production plays an important role in the economy of Rwanda in general and in Nyabihu

in particular. Favorable ecological conditions in North West motivate the production of

the crop. Potato production is also motivated by domestic consumption and the economy.

Meeting this objective requires efficient utilization of scarce resources. However, there

could be intervening variables which may hinder farmers to realize this objective.

Despite the efforts directed at improving Irish potato production over the years, the

problem of low production remains a major challenge .The low production is due to

inefficient use of resources ,inadequate supply of quality seed, low output prices, lack of

extension and inadequate of financial resource. Now the question arises: how can potato

production in Rwanda especially in Nyabihu District be increased? One approach that

can be used to answer this question is that of utilization of scarce resources efficiently.

This study will focus on two questions: first, whether farmers are not technically efficient

in potato production and second, which factors determine their level of efficiency?

Answers to these two questions provide a clue on how we can assist Potato growing

farmers to be efficient and allocate their resources employed in potato production. Given

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population growth rates, urbanization rates, and consumption preferences, demand for

potatoes in Rwanda is expected to increase by 200-250 percent by the year 2020 (Mellor,

2002). However, the problem facing Rwanda today is to produce enough food to feed its

nine millions of people which is not keeping pace with population growth under

smallholder constraints of limited inputs and land. Thus, there is a need to examine

technical efficiency of potato production in Nyabihu District and identify factors

influencing technical efficiency.

1.4 Purpose and Objectives of the study

The purpose of this study is to examine the level technical efficiency among smallholder

potato production and determine factors influencing technical inefficiencies in Nyabihu

District, Rwanda.

Specific Objectives of the study are:

1. To estimate the level of technical efficiency of smallholder potato producers in

Nyabihu District.

2. To assess the socio- economic factors influencing technical efficiency among potato

producers in Nyabihu District, Rwanda

1.5 Hypotheses

The hypotheses to be tested in this study are:

1 The smallholder potato farmers in Nyabihu District are not technically efficient.

2 Socio-economic factors such as, household size, education, sex, maritial status, farm

size, experience in farming, access to credit, extension services, and do not influence

technical efficiency of potato production in Nyabihu District.

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1.6 Justification of the study

A study on Technical Efficiency of Irish potato is justified by a lot of importance given to

agriculture in the Rwanda economic plan known as Vision 2020. It is also justified by

identified great role that agriculture is expected to play to meet Millennium Development

Goals one (MDG1) target.

Its plays an important role both as food and cash crop in the country in general and

Nyabihu District in particular. With 57,000 ha under cultivation, the potato sector is a large

and dynamic segment of agriculture. Hundreds of thousands of Rwandan farmers across the

country are engaged in commercial and subsistence cultivation. Irish potato is a major crop

widely grown in the Rwanda Northern and Western provinces where population depends

on the farming activities for their livelihood.

Annual national production level stands at 1,073,000 tones while and annual

consumption is a very high 125 kg per person, making potato the country's second most

important source of calorie intake after cassava. It is characterized by a high demand for

domestic markets; especially in urban areas.

Moreover, the technical efficiency study will play a significant role in providing useful

information regarding economic inefficiencies in production and helps to identify those

factors, which are associated with inefficiencies that may exist. Therefore, it is expected

from this study to generate adequate understanding of the issues that might lead towards

taking appropriate actions for improvement of efficiencies and the identification of the

extent of inefficiencies as well as the factors associated with them. Furthermore, the

study also came at a time when the efficiency of smallholder family farms is highly

disputed in Rwanda.

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CHAPTER TWO

LITERATURE REVIEW

This chapter reviews previous literature based on technical efficiency. It provides a

theoretical background on the concepts of technical efficiency as well as the socio-

economic factors influencing it. The present study will help to fill the gap, where no such

study exists that explores efficiency in Irish potato production in Rwanda.

2.1. The Concept of Efficiency Yotopolous et al (1967) relates the efficiency of the firm to a comparison between

observed and optimal values of its outputs and inputs. If the optimum is defined in terms

of production possibilities, the resulting comparison measures technical efficiency. If the

optimum is defined in terms of behavioral goals of the firm(e.g. profit maximization and

cost minimization),then efficiency is economic and is measured by comparing a firm’s

observed and optimum achievement of goals(e.g. profit, revenue and cost) subject to the

appropriate consideration of technology and prices.

The analysis of efficiency dates back to Knight (1933), Debreu (1951) and Koopmans

(1951). Koopmans (1951) provided a definition of technical efficiency while Debreu

(1951) introduced its first measure of the ‘resource utilization’. Following on Debrew in a

seminal paper Farrell (1957), provided a definition of frontier production functions,

which embodied the idea of maximality.

Farrell (1957) proposed that the economic efficiency of a firm consists of two

components: technical efficiency and allocative efficiency. Technical efficiency refers to

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the ability of a firm to produce maximal potential outputs from a given amount of input

or to use a minimal amount of inputs in order to produce a given amount of output.

Allocative efficiency represents the ability of a firm to utilize the cost-minimizing input

ratios or revenue-maximizing out-put ratios. A firm is allocatively efficient if it uses the

optimal combination of inputs with respect to their prices. First-order conditions from

revenue maximization can be used to determine optimal output ratios based on output

prices and marginal costs.

Heady(1952) defines the efficiency of resource use as the point at which net returns from

a single technical unit are at a maximum when the marginal cost of the resource is equal

to the marginal value product of the resource. He further states that farmers do not always

extend resource use to this point of efficiency use. This inability to equate marginal cost

of resources, either for technical unit or for the farm as a business includes three

considerations; (i) Lack of knowledge or principles, (ii) lack of knowledge of the relevant

input-output relationships and cost structures, (iii) the uncertainty of future prices and

yields and the existence of severe capital limitations

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2.2 Approaches to measuring efficiency

The literature on the measurement of efficiency is divided into two major approaches that

use either parametric or non-parametric frontiers. The frontier defines the limit to a range

of possible observed production (cost) levels and identifies the extent to which the firm

lies below (above) the frontier. In the parametric frontier analysis the technology of a

decision making unit is specified by a particular functional form for the cost, profit or

production relationship that links the decision making unit’s output to input factors (Delis

et al., 2008).

The most widely applied technique is the Stochastic Frontier Approach (SFA) originally

proposed by Aigner et al., (1977) and Meeusen et al., (1977) .The model is defined by

iiii uvxfY −+= );(ln β , ………………, i = 1,2,…N……………………………(2.1).

The random error, Vi, accounts for measurement error and other factors, such as the

weather, strikes luck, etc, and µi is one -sided component representing technical

inefficiency. Under the SFA, the error term is split into two components, allowing for

both random effects and frontier efficiency, where the random effects usually follow a

normal distribution and the inefficiencies a truncated normal distribution. The non

parametric approaches to efficiency measurement include the Data Envelopment

Analysis and the Free Disposal Hull. The Free Disposal Hull was developed by Deprins

et al., (1984) while the DEA method was first used by Charnes et al., (1978).

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2.3 Concept of Data Envelopment Analysis (DEA) Data Envelopment Analysis (DEA) is non parametric method of measuring efficiency

that uses mathematical programming approach to frontier estimation rather than

regression. This approach based on the work of Farell (1957) and Fare et al. (1994) has

since been improved upon and extended programming method of DEA, which compares

by Battesse (1992) and Coelli (1995). Charnes et al. (1981) introduced the method of

Data Envelopment Analysis (DEA) to address the problem of efficiency measurement for

Decision Making Units (DMUs) with multiple inputs and multiple outputs in the absence

of market prices.

However, the DEA approach suffers from criticisms that it takes no account of the

possible influence of measurement errors and other noise data that are common in

agriculture, since all observed deviations from estimated frontier are assumed to be the

result of technical inefficiency (Coelli and Battese, 1996). Nevertheless, parametric and

non parametric models differ in two ways. First, the two models differ on assumptions of

the distribution of the error term that represents inefficiency. Second, they differ in the

way the functional form is imposed on the data.

Parametric methods impose functional and distributional forms on the error term whereas

the non-parametric methods do not. An important drawback of the parametric approaches

is that they impose a particular functional form (and hence all its associated behavioral

assumptions), which predetermines the shape of the frontier. If the functional form is

incorrectly specified, the estimated efficiency may be confounded with significant bias.

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2.4 Technical, Allocative and Economic Efficiency Measurement of economic efficiency requires an understanding of the decision making

behaviour of the producer. A rational producer, producing a single output from a number

of inputs, x = x1……xn, that are purchased at given input prices, w = w1…..wn and

operating on a production frontier will be deemed to be efficient. But if the producer is

using a combination of inputs in such a way that it fails to maximize output or can use

less inputs to attain the same output, then the producer is not economically efficient.

A given combination of input and output is therefore economically efficient if it is both

technically and allocativelly efficient; that is, when the related input ratio is on both the

isoquant and the expansion path (Farrell 1957).

These contentions are best illustrated in the figure 2.1 below. This figure, indicates that

AB is an isoquant, representing technically efficient combinations of inputs, x1 and x2,

used in producing output Q. AB is also known as the ‘best practice’1production frontier.

DD' is an iso-cost line, which shows all combinations of inputs x1 and x2 such that input

costs sum to the same total cost of production. However, any firm intending to maximize

profits has to produce at Q', which is a point of tangency and representing the least cost

combination of x1 and x2 in production of Q. At point Q' the producer is economically

efficient.

1 Coelli (1995) indicates that the production function of the fully efficient firm ‘best practice’ is not known in practice, and thus it must be estimated from the sample of the industry concerned.

12

Figure 2.1: Concept of Technical and Allocative Efficiencies

Source: Coelli, et al, 1998

Turning to measurement of technical, allocative and economic efficiency, the same figure

3 is employed. Suppose a farmer is producing its output depicted by isoquant AB with

input combination level of (X1and X2) in figure 2.1. At this point (P) of input

combination the production is not technically efficient because the level of inputs needed

to produce the same quantity is Q on isoquant AB. In other words, the farmer can

produce at any point on AB with fewer inputs (X1 and X2) in this case at Q in an input-

input space. Therefore, the point Q is technical efficient because it lies on the efficient

isoquant .The degree of technical efficiency (TE) of such a farm is measured as TEi

=OQ/OP. The proportional OQ/OP is reduction of all inputs that could theoretically be

achieved without any reduction in output. In figure 2.1, DD' represent input price ratio or

iso-cost line, which gives the minimum expenditure for which a firm intending to

maximize profit should adopt.

x 2/y

R > Q

P

Q'

2

x1/y

B

D

O

A

D’

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The same farm using (X1 and X2) to produce output P would be allocatively inefficient in

relation to R. Its level of allocative efficiency( AE) is represented by OR/OQ = AEi ,

since the distance RQ represents the reduction in production costs if the farmer using the

combination of input (X1 and X2) was to produce at any point on D D', particularly R

instead of P. The overall (economic) efficiency (EEi) is measured as the product of

OQ/OP and OR/OQ, which is OR/OP. EEi = OQ/OP * OR/OQ = OR/OP. This follows

from interpretation of distance RP as the reduction in costs if a technically and

allocatively inefficient producer at P were to become efficient (both technically and

allocatively) at Q'. These forms reflect alternative behavioral objectives (i.e. profit

maximization or cost minimization) and can account for multiple outputs (Coelli, 1995).

2.5 Technical Efficiency: Empirical Application

This section presents a review of some of the technical efficiency studies .The stochastic

frontier production function (SFP) was independently proposed by Aigner, et al., (1977)

and Meeusen and Van den Broeck (1977). Some of the main researchers who have

utilized the stochastic frontier approach are: Battese and Coelli (1995); Battese (1996);

Abdulai and Huffman (2000); Thiam, et al., (2001); Awudu and Eberlin (2001); Gautam

and Alwang(2003); Khairo and Battese (2005). Many studies have been carried out on

technical efficiency in Africa and beyond. Lingard et al., (1983) applying a two-

component model to panel data estimated a bias free agricultural production function for

the Philippine rice farmers in Luzon District.

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The study showed that area was dominant in earlier years when the technology was

introduced, while other variables (such as irrigation, fertilizers and chemicals) became

significant overtime, reflecting full adoption of the technology.

Banik (1994) carried out a study on technical efficiency of irrigated farms in a village of

Bangladesh and used a stochastic production frontier. He used a Cobb-Douglas function

and used the Maximum Likelihood estimates (MLE) method to estimate the parameters

of the stochastic frontier Cobb-Douglas production function. The index of the technical

efficiency level for each individual farm was calculated estimating the one side error

component. The results showed that 88 out of 99 farms had a technical efficiency of 71

percent or above. A very interesting finding was that ten out of thirteen most efficient

farms belonged to the category of small farms. The study also revealed that owner-tenant

farms were technically more efficient than owner farms.

Panda (1996) used a frontier production function which he derived from Cobb-Douglas

production function and estimated by Corrected Ordinary Least Square (COLS) method.

Corrected Ordinary Least squares (COLS) models is among the most commonly used

parametric methods such as ,Ordinary least squares (OLS), and Stochastic Frontier

Analysis (SFA). In other words, the SFA models take both inefficiency and random noise

into account. When using COLS it is good practice to perform quantile analysis. Quantile

analysis helps to overcome the possible effect of outliers on the estimated mean allowing

the analyst to detect the presence of performers on specific or extreme quantiles such as

the lower (25%) or the upper (75%) quantiles.

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From the estimated equation, Timmer’s measure of technical efficiency and Copp’s

measure of allocative efficiency of various resources utilized in sericulture farms were

examined. The study revealed that the economics of sericulture was highly profitable

both in the traditional and non-traditional areas. The study also identified major

constraints in sericulture development as being inadequate trained manpower.

Kakhobwe (2007) carried out an analysis of technical efficiency of mixed intercropping

and relay cropping Agroforestry technologies in Zomba district in Malawi and a

stochastic production model of parametric approach specified by Battese and Coelli

(1995) to evaluate technical efficiency of Mixed and Relay cropping Agroforestry

Technologies and identify factors that determine the technical efficiency of farmers.

The results revealed that larger proportion of the farmers practicing, and relay cropping

Agroforestry technologies and NA produce maize below their frontier levels implying

that farmers did not effectively use their resources in maize production. The study further

revealed that age of household head and land fragmentation were the determinants of

technical efficiency of relay cropping agroforestry technology.

Belbase and Grabowski (1985) used corrected ordinary least squares (COLS) technique

to measure technical efficiency of farmers in Nuwakot District in Nepal.The

appropriately adjusted (removing the outliers) results showed that the Nepalese farmers

were operating close to the technical frontier. The factors contributing positively to

16

technical efficiency were: nutrition levels, family incomes and education. The structure

(farm size) of the farms was taken as given, yet as noted by Mbowa (1996), the variable

bears a significant influence on technical efficiency. Further, the Belbase and

Grabawoskis’ study did not deal with allocative inefficiency.

Ahmed et al., (2004) carried out a study on Cotton Production Constraints in Sudan:

Economic Analysis Approaches”. The main objective of the economic study was to

identify, analyze and evaluate the major constraints of cotton production in the Gezira

Scheme. To analyze technical efficiency the study employed a stochastic frontier model.

Stochastic Production Frontier Analysis results revealed that 48 percent of cotton yield

variability was due to tenant and scheme management specific factors. And that 25

percent of the variability was due to the tenants’ technical inefficiency and 23 percent is

due to the scheme management’s inefficiency.

Yilma (1996) used three different approaches to estimate smallholder efficiency in coffee

and bananas namely, deterministic parametric, stochastic frontier approaches and DEA in

Masaka district, Uganda. The deterministic parametric approach showed differences in

mean scores of efficiencies in coffee and generally food production. The coefficients

estimated under deterministic parametric frontier model showed lower efficiency than the

stochastic frontier model, agreeing with many earlier studies (Kalirajan and Obwona,

1994 and Lingard et al., 1983). Nevertheless, irrespective of the approach used, all

farmers were found not to be producing on the frontier.

17

Mbowa (1996) used DEA to examine resource use farm efficiency on small and large-

scale farms in sugarcane production in Kwazulu-Natal. The study results showed that

small-scale farmers were technically inefficient than large-scale producers and concluded

that the size of farm operation affects level of efficiency attainable.

Abedullah (2006) did a study on “Technical Efficiency and its Determinants in Potato

Production, Evidence from Punjab, Pakistan” using Cobb-Douglas stochastic production

frontier approach. The result showed that potato farmers are 84 percent technical

efficiency implying significant potential in potato production that can be developed.

There was high correlation between irrigation of the potato crop and technical efficiency.

However, it is different in terms of type of dataset used, focus area, some regressions

used as well as geographical location.

Obwona (2006) estimated a translog production function to determine technical

efficiency differentials between small- and medium-scale tobacco farmers in Uganda

using a stochastic frontier approach. The results showed that, credit accessibility

extension services and farm assets contribute positively towards the improvement of

efficiency. One major drawback of this study is the inability of the author to show in

clear terms whether there is any differential in efficiency between the two groups of

farmers. The estimated efficiencies were explained by socioeconomic and demographic

factors. The results showed that, credit accessibility extension services and farm assets

contribute positively towards the improvement of efficiency. One major drawback of this

18

study is the inability of the author to show in clear terms whether there is any differential

in efficiency between the two groups of farmers.

Olorunfemi et al., (2006) Technical efficiency differentials in rice production

technologies in Nigeria. The study examine technical efficiency differentials between

farmers planting traditional Rice and those planting improved verities in Nigeria,

estimated a Cobb–Douglas production function through a method of ordinary least square

(OLS) and discovered that labour and seed inputs were inefficiently utilized. Farm size

(scale of operation) and the level of technology were not taken into consideration.

Elibariki (2005) this study describes the technical efficiency of sugarcane production and

the factors affecting in Tanzania. This efficiency was estimated using the Cobb-Douglas

production frontier assumed to have a truncated normal distribution. The study

determined and compared the level of technical efficiency of out grower and non-out

grower farmers, and examined the relationship between levels of efficiency and various

specific factors. The results of the estimation showed that there were significant positive

relationships between age, education, and experience with technical efficiency.

Nyagaka (2009) carried out a study on Economic Efficiency of Smallholder Irish

Potato Producers in Kenya: A Case of Nyandarua North District using stochastic frontier

function. The Tobit model Tobit model is used to derive efficiency indices as a function

of a vector of socio-economic characteristics and institutional factors.

19

The result show decreasing returns to scale in production, education, access to extension,

access to credit and membership in a farmers association positively and significantly

influence economic efficiency. According to our knowledge there exists very little

literature dealing with technical efficiency in Rwanda. One study found is for Byiringiro

and Reardon (1996) “Investigated the effects of farm size, soil erosion and soil

conservation investments on land and labour productivity and allocative efficiency in

Rwanda”. The authors concluded that there is a strong inverse relationship between farm

size and land productivity. Furthermore, for small farms, there was evidence of

inefficiency in the use of land and labour, the cause being attributed to factor market

access constraints.

20

CHAPTER THREE

METHODOLOGY

This chapter provides information on methods adopted for data analysis in the study as

well as sampling design, sample size determination and data collection procedure.

3.1 Analytical framework

3.1.1 Theoretical framework: Stochastic frontier production

For a long time, econometricians have estimated average production functions. It is only

after the pioneering work of Farrell (1957) that serious considerations have been given to

the possibility of estimating the so-called frontier production functions in an effort to

bridge the gap between theory and empirical work. (Aigner, Lovell and Schmidt, 1977).

According to Farrell, technical efficiency reflect the ability of the firm to maximize

output for a given set of resource inputs while allocative (factor price) efficiency reflects

the ability of the firm to use the inputs in optimal proportions given their respective

prices and the production technology.

Following Farrell’s (1957) work, there has been a proliferation of studies in the field of

measuring efficiencies in all fields. However over the years, Farrell’s methodology had

been applied widely while undergoing many improvements. And of such improvement is

the development of the stochastic frontier model which enables one to measure farm level

technical and economical efficiency using Maximum Likelihood Estimation (MLE) a

Correction of Ordinary Least Square (COLS). A stochastic model originally was

pioneered by Aigner and Chu (1968) who proposed a composed error term. Building on

21

the work of Aigner and Chu (1968) a stochastic frontier model was developed (Aigner, et

al., 1977, Meeusen and van den Broeck, 1977, Battese and Corra, 1977).

Following the specification stochastic production frontier can be written as:

( ) Niexi

ii fY .............,2,1, == εβ (3.1)

Where Yi is the yield of potatoes for the i-th farm, xi is a vector of k inputs (or cost of

inputs), ββββ is a vector of k unknown parameters, εi is an error term. The stochastic

production frontier is also called “composed error” model, because it postulates that the

error term εi is decomposed into two components: a stochastic random error component

(random shocks) and a technical inefficiency component as follows:

uv iii −=ε (3.2)

The model used in this paper is based on the one proposed by Battese and Coelli et al.,

(1995) and Battese et al., (1996) in which the stochastic frontier specification

incorporates models of technical inefficiencies effects and simultaneously estimate all the

parameters involved in the production function. The stochastic production frontier

functional form which specifies the production technique of the farmers is expressed as

follows:

iiii uvxfY −= exp);( β (3.3)

Where iY represents of potato output, which is measured in kilograms, ix represents the

quantity of input used in the production, iv represents random errors assumed to be

independent and identically distributed Ν(0, σν2) and iu represents the technical

inefficiency effects assumed to be non-negative truncated of the half-normal distribution

22

Ν(µ, σu2). The truncated-normal distribution is a generalization of the half-normal

distribution. It is obtained by the truncation at zero of the normal distribution with

mean µ, and variance,σ 2u . If µ is pre-assigned to be zero, then the distribution is half-

normal. Only two types of distributions are considered such as, half –normal and

truncated-normal distributions. These two distributions allow for a wider range of

distributional shapes but this comes at the cost of computational complexity.

This technique was developed by Coelli (1996) and has been used extensively by various

authors in estimating technical efficiency among crop farmers. The two error components

(v and u) are also assumed to be independent of each other. The variance parameters of

the model are parameterized as:

10;2

2222 ≤≤=+= γ

σσγσσσ and

s

uuvs (3.4)

The parameter γ must lie between 0 and 1. The maximum likelihood estimation of

equation (1) provides consistent estimators for theβ , γ, and σ 2s parameter, where,

σ 2s explains the total variation in the dependent variable due to technical inefficiency

(σ 2u ) and random shocks (σ 2

v ) together (Jondrow et al 1982).

The technical efficiency of individual farmers is defined as the ratio of the observed

output to the corresponding frontier output, conditional on the level of input used by the

farmer.

23

Hence the technical efficiency of the farmer is expressed as:

)exp(exp);(/)exp();(*iiiiiiiii uvxfuvxfYYTE −=−== ββ (3.5)

Where iY represents observed output and *iY represents frontier output. Farrell’s 1957

measure of technical efficiency ( iTE ), takes a value between zero and one. It indicates

the magnitude of the output of the ith farm relative to the output that could be produced

by a fully-efficient farm using the same input vectors.

3.2 Empirical model A number of functional forms exist in literature for estimating the production function

which includes the Cobb-Douglas (C-D) and flexible functional forms, such as

normalized quadratic, normalized translog and generalized Leontif. The C-D functional

form is popular and is frequently used to estimate farm efficiency despite its known

weaknesses of imposing several restrictions, including unitary elasticities of substitution,

constant production elasticities and constant factor demand elasticities (Fuss et al., 1978).

The translog model has its own weaknesses as well, but it has also been used widely (Ali

and Flinn, 1989; Wang et al., 1996). The main drawbacks of the translog model are its

susceptibility to multicollinearity and potential problems of insufficient degrees of

freedom due to the presence of interaction terms. The interaction terms of the translog

also don’t have economic meaning (Abdulai and Huffman, 2000). The stochastic frontier

production function model of the Cobb- Douglas function form is employed in this study

to estimate the farm level technical efficiency of potato growers in Nyabihu District.

24

This choice is made on the basis of the variability of agricultural production, which is

attributable to climatic hazards, plant pathology and insect pests, on the one hand, and on

the other hand, because information gathered on production is usually inaccurate since

smallholder farmers do not have updated data on their farm. In fact the stochastic frontier

method makes it possible to estimate a frontier function that simultaneously takes into

account the random error term and the inefficiency component to every farmer. The

stochastic frontier production function (SFPF) literature offers two approaches in

analyzing technical efficiency (TE). The first one is to use two-stage OLS estimation. In

the first stage of the OLS estimation, the production frontier is regressed and values for

technical inefficiency are derived subsequently. In the second stage, these derived

inefficiency values are regressed upon a vector of household and other socio-economic

variables (Kalirajan 1981; Pitt and Lee, 1981; Tadesse and Krishnamoorthy, 1997;

Abdulahi and Huffman, 2000). However, a caution is in order as far as this approach is

concerned.

This approach violates the distributional assumptions of the error terms. In other words,

the two-stage procedure lacks consistency in assumptions about the distribution of the

inefficiencies. In step one, it is assumed that inefficiencies are independently and

identically distributed in order to estimate their values. In step two, estimated

inefficiencies are assumed to be a function of a number of firm-specific factors, violating

the assumption in step one (Coelli, Rao, and Battese, 1998). The second approach of

SFPF estimation is using a single-stage maximum likelihood model (Battese and Coelli,

1995). In this study, the second approach is used because of its advantages. Unlike the

25

two-stage approach, it does not violate the distributional assumption of the error terms.A

solution to these problems would be to estimate both (C-D and Translog) and then use the

results of the values of the Loglikelihood at the set critical value to reject or accept one

model over the other. Battesse and Safraz (1998) tried both models and found that the C-

D production function model was an adequate representation of the data. This study runs

both the C-D and translog frontier profit function models. Both of these models have

been widely used in Asia and Africa (Ali and Flinn, 1989; Saleem, 1988; Abdulai and

Huffman, 2000 and Rahman, 2002, 2003) as earlier noted.

We define the empirical form of the stochastic production function in Translog and C-D

respectively represent in (3. 7) and (3.9) equations: For Translog production function is

expressed as shown in equation 3.6. The specific model estimated from this general case

by transforming all variables to natural logarithm from (Murillo-Zomaro,2004).

( )( )( )jiiijkxxx

ki eYlnln))(ln2/(

210

221 ..., βββββ ΧΧΧ= …………………………..( 3.6)

The technical efficiency effect model (Coelli and Battesse; 1995) in which both the

stochastic frontier and factors affecting inefficiency are estimated simultaneously is

specified as follows:

In linear Translog function form:

iij

jiii i

ii uvXj

Xij

XijQ −+++= ∑∑ ∑== =

6

1

6

1

6

12

10 lnlnlnln ααα

(k=1,2,,,,,,,,6)………………………….(3.7)

Where ln designates a natural logarithm, and subscripts i and j, respectively, represent

the inputs i used by farm j.

26

Further:

Q = potato output of in Kgs,

X1 = total area under potato,

X2= the total quantity of seeds used for potato production (Kgs)

X3= the amount of family labour, (in person-days).

X4= the amount of family labour (in person-days).

X5= the total quantity of chemical fertilizer used in potato (in Kg)

X6= the total quantity of pesticide fertilizer used in pot

v = is the random error, µ is inefficiency effect and αi are unknown parameters to be

estimated.

The general form of Cobb-Douglas production function was specified as follows:

∏=

−=6

10

i

uvi eXQ iαα …………………………………………………………….(3.8)

The model was estimated using linear Cobb-Douglas Production form which is presented

as follows:

Ln Q = α0 +α1ln X1 + α2lnX2 + α3lnX3 + α 4lnX4 + α 5lnX5 + α6lnX6 + α7lnX7 + Vi – Ui

……….(3.9)

Where: Y = Irish potato Output.

X1 = Area under potato (ha)

X2 = quantity of seeds used (Kg)

X3 =Hired Labour (man-day)

X4 = Family labor (man- day)

X5 = Fertilizer (kg)

X6 = pesicide (Kg)

27

α 0, α 1, α 2, α 3, α 4, α 5, α 6, = Parameters to be estimated.

The Cobb Douglas model, which was found to be an adequate, used for this study is

specified as follows:

)9.3.......(................................................................................ln

.lnlnlnlnlnlnln

6

543210

ii

i

uvPESTDE

FERTFAMLABORHIRLABORSEEDAUPQ

−+++++++=

ααααααα

The variables included in the stochastic production model and their expected signs are

Summarized in table.

Table 3. 1 Variables in the stochastic Cobb-Douglas production model Variables Descriptions Measurement

unit Sign

(AUP) Area under Potato

Represent the total farm size in hectare under potato in season A &B. (September 2009- February 2010)

Hectares +

Seed

Quantity of potato seed used for Potato production in season A& B

(Kgs) +

(HIRLABOR) Hired Labor

Hired labour per hectare Man-day +

(FAMLABOR) Family Labor

Family labour per hectare Man-day

(FERT) Fertilizer

Chemical used (Kg) +

(PESTDE) Pesticide

Pesticide fertilizer used ( Kg) +

Q: Potato output in season A&B

Potato out (Kg) Represent the total farm area in hectare operated by the potato growers

Kgs Dependent

Source: Author’s presentation

28

ν and µ are as defined earlier

iα = are unknown parameters to be estimated

All inputs in the Cobb-Douglas production function are expected to have a positive

impact on potato output since an increase in each (or all of) the inputs can lead to

increased output.

We defined the Technical inefficiency (TIE) model in equation (3.8) this was done to

address the Second objective.

)10.3..(..........................................................................................8

10 ∑

=

++=i

iiii Z εαµ α

Where

µi = Inefficiency effects

αi = Intercept term

Z1 = Family size of farmers growing potato (Number of household farm members)

Ζ2 = Farmer level of Education of a farmer (Year of formal education)

Ζ 3 = Farming Experience of the farmer in potato (Year of farming)

Ζ4 = Farm size of farmer in hectares

Ζ5 = Marital status of the farm

Ζ6 = Gender of the farmer .Measured as a dummy variable 1 for male,0 otherwise

Ζ7 = Credit accessibility. A dummy 1 if farmer received credit in the survey year, 0

otherwise Ζ8 = Extension contact in the year.

A dummy 1 for farmers visited by extension agents in the survey year, 0 otherwise.

Where 1Z ,. Ζ 2....and Z8 are Family size of farmer growing potato, Farmer level of

educational, farming experience in growing potato, farm size of farmer, Martial status of

29

the farm, Gender of the farmer access to credit, farmers age in year, Extension contact in

the year the farm area respectively. These are included in the model to indicate their

possible influence on the technical efficiency of the farmer. The iα ’s are parameters to

be estimated. Table 3.2 shows a detailed description of all the variables in the model

together with their expected signs.

Table 3.2: Description of variables included in the Inefficiency Model and their expected signs List of Variables Descriptions Expected sign

ui Inefficiency effects

0α Intercept term

1Z Farmer family size (Number of household farm

members

+ve

2Z Farmer level of Education of a farmer (Year of

formal education)

+ve

3Z Farming Experience of the farmer in potato (Year

of farming)

+ve

4Z Farm size of farmer in hectares +ve

5Z Maritial status of the farm ve±

6Z Gender of the farmer .Measured as a dummy

variable 1 for male,0 otherwise

-/+ve

Z7 Credit accessibility. A dummy 1 if farmer

received credit in the survey year, 0 otherwise

+ve

Z8 Extension contact. A dummy 1 if farmer received

extension agents in the survey year, 0 otherwise

+ve

Source: Author’s presentation, 2010

30

3.3 Data needs and Source

This section gives a brief description of the data collection instrument and the sampling

procedure. The study used of both primary and secondary data. Primary data was

obtained directly from respondents (farmers) through face-to-face interview using multi-

stage sampling while secondary data were obtained from books, journals and records of

Ministry of Agriculture.

Data were collected through trained enumerators using pre-tested questionnaire. The

survey was conducted during the month of April and May 2010. The questionnaires

included issues on socio-economic characteristics such as household size, level of

education, gender, marital status, experience, farm size, access to credit, and participation

in extension services.

3.3.1 Determination of the sample size

The target population of this study were smallholder farmers involved in potato farming.

To get the sample size, n, needed to estimate a population proportion, p. The following

formula by Edriss, (2003) was used to compute the sample size.

2

2 )1(

e

ppzn

−=

Where n is the sample size, where Z is the desired Z-value yielding the desired degree of

confidence, p is an estimate of the population proportion, and e is the absolute size of the

error in estimating p that the researcher is willing to permit. In this study a p-value of 0.1

was used. This is because of the fact that almost 90 percent of smallholder farmers in the

study area produce potato. The study used 95 percent level of confidence (Z= 1.96 for a

31

two tailed test), with an allowable error of 0.05. The sample was calculated as shown in

the equation below;

13805.0

1.0)1.01(96.12

2

=−=n ………………………………………………(3.11)

The questionnaires were pretested four days to ensure confirmation with the desired

response and administered to household. The tested questionnaires were used for

corrections and production of final questionnaires which were used for collecting

household data.

3.3 .2 Sampling Procedure Nyabihu district and 3 sectors Kabatwa, Mukamira and Karago (sector which is the level

of administration) was chosen purposively, as a representative of volcanic zone where

Potato is major potato activities. The sample was selected randomly from three different

sectors. In this study, two- stage sampling technique was randomly select. In the first stage,

5 cells (the smallest politico-administrative unit of the country) were randomly selected

from each sector giving a total of 15 from the 3 cells and these were Myunga, Gihorwe,

Rugarama, Cyamvumba, Batikoti, in Kabatwa Sector while Rugeshi , Jaba, Rurengeri,

Rubaya, Kanyove, of Mukamira sector and Kadahenda, Gihirwa, Busoro,Cyamabuye,

Busoro in Karago .

The secondary stage, the villages was randomly selected. From each village 10

households farmers were selected randomly from a list provided by of sector’s office. A

total sample of 50 households was collected from each cell, making a total of 150

households. A total of 150 farmers were interviewed, but were two non-respondent hence

32

148 farmers were interviewed. However, 123 were consisted in this study because 25

were dropped for lack of adequate missing data in the some sample of household.

3.3.3 Data Preparation and Analysis

Data analysis of this study involved both descriptive (percentages, means, standard

deviation) and regression using STATA and Statistical Package for Social Scientist

(SPSS) computer programs. The data was then transferred to Stata in which econometric

analyses were carried out.

A Cobb-Douglas stochastic production function was estimated using the single-step.

Procedure suggested by Kumbhakar et al. (1991).This procedure combines the two-stage

procedure into one and produces maximum likelihood estimates of the stochastic

production function. The procedure is superior to the two-stage procedure because it does

not violate the assumption that the inefficiency effects are independently and identically

distributed (Battesse and Coelli, 1995).

3.4 The Study Area

The district is situated in the Northwest of Rwanda in West province with 512.5 square

kilometers. The population of Nyabihu district is estimated about 280.210 persons while

99 percent leave in rural area with 541 square kilometers of density. (District report

2007). Agriculture is the main activity in the district with potato as the dominant farming

activity followed by maize. The district is one of the major Irish potato growing districts

of Rwanda with the approximately 8241 ha of land under Irish potato cultivation.

33

Nyabihu district is characterize by reliable rainfall with annual amount of 1400 mm. The

rainfall is bimodal and can reach 150mm/month in months of March and May. The Mean

maximum temperature is 15oC well as the mean minimum temperature ranges between

10 to 16oC. The climate is conducive to rich and varied agricultural production where

agro-ecological situations are very diverse and include rich soils derived from the

volcanics.

Figure 3.1: Administrative Map of Nyabihu District

MURINGA

JENDA

RAMBURA

KABATWA

JOMBA

BIGOGWE

RUGERA

SHYIRA

KARAGO

RUREMBO

MUKAMIRAKINTOBO

MURINGA

JENDA

RAMBURA

KABATWA

JOMBA

BIGOGWE

RUGERA

SHYIRA

KARAGO

RUREMBO

MUKAMIRAKINTOBO

Secteur deBIGOGWEJENDAJOMBAKABATWAKARAGOKINTOBOMUKAMIRAMURINGARAMBURARUGERARUREMBOSHYIRA

Parc National des VolcansLimite de secteurLimite de distict

S

N

EW

CARTE ADMINISTRATIVE DU DISTRICT DE NYABIHU

3 0 3 6 Kilometers

©Institut National de la Statistique du Rwanda, Mars 2006

34

Nyabihu district is bordered by Rubavu district in West, in North, Democratic Republic

of Congo and Musanze district in East Gakenke district and south Ngororero and Rutsiro

districts. It is divided into 12 administrative sectors2 that is Bigogwe, Jenda, Jomba,

Kabatwa, Karago, Kintobo, Mukamira, Muringa, Rambura, Rugera, Rurembo and Shyira

and 73 cells3.

3.5 Testing of Multicollinearity

Multicollinearity refers to the presence of linear relationships or near linear relationship

among explanatory variables in OLS assumption violation of a regression function

(Gujarati, 2005). Multicollinearity can be caused due to wrong model specification and

the use of lagged variables in a regression model. Economic variables tend to move

together hence causing multicollinearity. For example in times of boom production and

wages are high and the reverse is true in times of recession (Gujarat and Sangeetha,

2007).

However, the OLS estimated coefficients are always unbiased. Due to unbias coefficients

may be statistically insignificant thus causing wrong signs and high R2 at different

times. As a result, hypothesis testing becomes weak so that diverse hypotheses about

parameter values can be rejected. Therefore it was important to evaluate the existence of

multicollinearity. Kennedy, (1985) also states that a value of 0.8 or higher in absolute

terms in one of the correlation coefficients indicates a high correlation between the

independent values in which it refers. Based on this criterion, the correlation coefficients

do not exist in relation to multicollinearity. See Appendix 3 2 The sector ( Umurenge) is the next level of administration in the contry 3 The cell (Akagari ) is the smallest politico-administrative unit of the country

35

CHAPTER FOUR

RESULTS AND DISCUSSIONS

This chapter presents the data and discusses findings of the study. It is organized as

follows; section one presents brief description of important household characteristics of

potato production, section two deals with technical efficiency estimates and factors

explaining the observed inefficiency while section contains discussions of results of the

study.

4.1. Householder Characteristics This section discusses the characteristics of the small holder farmers who are involved in

potato production. The specific household characteristics considered here were:

household size, gender, marital status, education and experience in potato production of

the household head.

4.1.1 Household size Family size can explain the level of production through its effects on labor availability

and food consumption. Figure 4.1 below shows that household size among potato farmers

range between 3 to 12 persons with estimated average of 7 persons. This suggests that

they may have a reasonably large family size which may provide more family labor in

production than other households with different size. In other words, majority of the men

in that region are polygamous.

36

Figure 4.1: Family size

Family size in percentage

0

5

10

15

20

3 4 5 6 7 8 9 10 12

Number of persons in the household

Per

cent

age

Family size in percentage

Source: Author’s presentation, 2010

4.1.2 Gender and Maritial status

A total of 123 household heads from the district were retained in the sample (after

excluding 25 outliers). Table 4.1 shows that 73.1 percent were males involved in potato

production while 15.4 percent are females. Bagamba (2007) contends that men are

capable of doing more tedious work which is usually associated with farming than the

females. He also asserts that farms managed by men were expected to attain higher

technical efficiency than those that were managed by women.

37

Table 4.1 Farmer distribution according to gender and marital status

Sex Marital status

Single Married % Divorced Widowed Total

Male 3 90 73.1 1 0 94

Female 3 19 15.4 3 4 29

Total 6 109 88.6 4 4 123

Percentage 4.8 88.6 3.5 3.5 100

Source: Author’s presentation, 2010

The marital status of the households as illustrated in table 4.1 indicates that 88.6 percent

of the respondents were married well as 3.5 percent of farmers were divorced widows

while 4.8 percent were single. Various factors explain this gender difference engaged in

potato production. For example, women in rural areas are mostly involved in domestic

activities such as collecting water and firewood. Therefore, it may not be easy for women

to afford extra time to do field activities.

38

4.1.3 Education Level A positive relationship is expected between education level and management productivity

(DAtchoarena et al., 1983). A farmer’s level of education is expected to influence his

ability to adopt agricultural innovations and make decisions on various aspects of

farming. Education is therefore highly important for sustainable agricultural growth and

development. Figure 4.2 indicates that education level of respondents were low given that

those who attained formal education in primary were 35.7 percent and those of secondary

level were 2.4 percent.

The results also show that 56.9 percent of potato farmers did not complete primary

education. This is a challenge to the extension staff in the area to ensure that farmers are

trained on modern farming practices. Kalirajan Bravo-Ureta and Evenson (1984, 1994)

contend that the impact of education on efficiency is negative. Their argument is that

when a farmer gets access to better education, he or she may get better opportunities

outside the farming sector to pursue other income earning activities. Therefore, this

reduces labor availability for a farm production in the household thereby lowering

efficiency.

39

Figure 4.2: Education level of household head

Education level of household

56%

36%

5%

3%

0%

Never went to school(56.9)

Primary(35.7)

Tertiary(4.8)

Secondary(2.6)

University(0)

Source: Author’s presentation, 2010

4.1.4 Area under Potato Production Land is a limiting factor of production in Rwanda. The area under potato production

ranges from 0.2 ha to 1.5 ha. The average potato farm area in the study area was 0.34

hectares. The largest cultivatable land for potato production is between 1 and 1.5

equivalents to 67.4 percent of the total land well as that land between 0.5-09 hectares is

the smallest and covers 22.7 percent of the cultivatable area .

40

Table 4.2 Potato Farm area category

Farm size Category(ha) Percentage

0.20-0.49 9.7

0.5-0.9 22.7

1- 1.5 67.4

Total 100

Source: Author’s presentation, 2010

4.1.5 Experience of growing potato

The results of this study as presented in table 4.3 shows that 86.2 percent had farming

experience of growing potato of more than 10 years. On the average all farmers had an

experience of 12 years in potato production. Kabede (2001) argues that increasing

farming experience lead to better assessment of importance and complexities of good

farming decision including efficient use of inputs.

41

Table 4.3 Experience of farmer growing potato

Source: Author’s presentation, 2010

4.1.6 Extension services Table 4.4 shows that 63.4 percent of farmers confirmed that extension agents had visited

them in September 2009 and March 2010 thus providing them basic agricultural skills

while 36.5 percent of the farmers were not able to access extension workers. Farmers

provided with basic agricultural skills were taught modern agricultural technology for

input use and disease control.

Experience of farmer growing potato (Year) Percentage

1-4 1.6

5-8 8.1

9-10 4.0

>10 86.2

Total 100

42

Table 4.4 Extension service visit

Extension services visits Percentage

Yes 63.4

No 36.5

Total 100

Source: Author’s presentation, 2010

4.1.7 Accessibility to credit The results of the study in table 4.5 showed that 89% of the respondents did not have

access to any form of credit while only 11.3% of the farmers had access to credit. Access

to credit improves problem of liquidity and enhances use of agricultural inputs in

production. Lack of credit facilities affected inputs acquisition especially among cash

constrained farmers. Farmers’ accessibility to credit through credit cooperatives can

reduce constraints encountered in production hence increasing the efficiency of farmers.

Table 4.5 Distribution of farmer to access to credit

Access to credit of the farmer Percentage

Yes 11.3

No 88.6

Total 100

Source: Author’s presentation, 2010

43

4.2 Estimation of Technical efficiency in potato production In the analyses of technical efficiency and its determinants, it is necessary to test the

presence of inefficiency in the production of the sample households. The test was carried

out by estimating the stochastic frontier production function. Likelihood-ratio test was

used to test null hypothesis of no technical inefficiency. The test statistics were computed

automatically when the frontier model was estimated using STATA.

4.2.1 Output and input variables in potato production The summary of the production function variables is presented in Table 4.6. The result

indicates that, the mean output per farmer in potato production was about 16,155 kg. The

analysis of the inputs revealed that the average farm size under potato production ranged

from 0.48 ha to 8 ha per farmer of minimum and maximum size of hectares of land

respectively. The mean hired labor was 79.72 man-days while family labor was 8.16

man-days. This shows that potato farmers depend heavily on hired labour to do most of

the farming operations. Labour constitutes the most important input into smallholder

agricultural production in Nyabihu.

The average amount of fertilizers used and pesticide applied was 18.16 Kg and 20.46 kg

respectively. The use of pesticides has been observed as a major labor saving device as

the labor requirement for weeding always accounts for a high proportion of the total farm

cost of labor in potato production. The average quantity of seeds for sampled farmers

planted was 3032.94 kg. The quantity and type of seed planted by potato farmers has a

lot of implications for yield realized.

44

Table 4.6 Summary descriptive statistics of output and input variables in Potato production (Kg, ha, man-day) Variable Mean Std Minimum Max Sample size

________________________________________________________________________ Source: Author’s presentation, 2010

4.2.2 Hypothesis Testing and Model Robustness

In order to select the best specification for the production function (Cobb-Douglas or

translog) for the given data set a hypothesis tests was conducted for the parameters of the

stochastic production frontier model using the generalized likelihood-ratio statistic “LR”

defined by

( )( )

−=

HLHLLR

1

0ln2 (4.1)

Total potato

production(Kg)

16.15 30.50 60 250.00 123

Area under potato

production (ha)

1.7 0.93 0.48 8 123

Seed quantity( Kg) 3032.94 4596.88 80 3000 123

Hired labor (Man day) 79.72 62.85 0 212 123

Family labor (Man

day)

8.16 21.70 0 107 123

Fertilize(Kg) 18.43 10.73 1 37 123

Pesticide (Kg) 20.46 9.65 1 37 123

45

where, L(H0) is value of the likelihood function of the Cobb-Douglas stochastic

production frontier model, in which the parameter restrictions specified by the null

hypothesis, H0 = βji = 0, (i.e. the coefficient on the squared and interaction terms of input

variables are zero) are imposed; L(H1) is the value of the likelihood function for the full

translog stochastic production frontier model where the coefficient of the squared and

interaction terms of input variables are not zero. If the null hypothesis is true, then “LR”

has approximately a chi-square (or mixed chi-square) distribution with degrees of

freedom equal to the difference between the number of parameters estimated under H1

and H0, respectively. We use the Cobb-Douglas (CD) and translog production functions

and on the basis of the test statistic it was discovered that the CD is the best fit to our

data set. On the basis of this test statistic we selected the Cobb-Douglas production

function.

In addition to the above evidence, the Cobb-Douglas (CD) functional form inspite of its

restrictive properties is used because its coefficients directly represent the elasticity of

production. It provides an adequate representation of the production process; since the

interest is efficiency measurement and not analysis of the production structure (Taylor

and Shonkwiler, 1986).

However a hypothesis to test whether the Cobb-Douglas production function is adequate

given the specifications of the translog model was made. Alternatively translog was

tested to find out if the coefficients of interaction and square terms in the translog

production function were zero. The results showed that the coefficients of area under

potato; hired labor; family labor; fertilize; pesticide were negative and statistically

insignificant indicating no relationship with output. Only coefficient of seed quantity

46

showed significant effect on output. The coefficients of the square term for the area

under potato production were size 0.5(lnX1)2, seed quantity 0.5(lnX2)

2 , fertilizer

0.5(lnX4)2 and those of the interactions of the area under potato production and hired

labor (InX8) area of potato production and pesticide (InX10) area under potato

production and family labor (InX11), fertilizer and family labor (InX20) are positive and

statistically significant showing direct relationship with output. This suggested that there

are no interactions amongst the variables.

Furthermore, robustness of the estimated models can also be indicated by the value of the

high log-likelihood function. The values of the log likelihood for the Cobb-Douglas and

translog production functions were -189.64 and -192.18, respectively thus the null

hypothesis that the Cobb-Douglas stochastic production frontier is an adequate

representation of the data was accepted, given the specifications of the translog stochastic

production frontier.

4.2.3 Test for the presence of inefficiency in potato production

The stochastic production function was used to test whether potato farmers were

technically efficient. This implies testing the null hypothesis that there is technical

efficiency in potato production which was rejected Ho : γ = 0 ( Table 4.8) and the

alternative hypothesis that there is technical inefficiency in potato production HA γ ≠ 0

which failed to reject HA. This was done using Likelihood ratio value compared to critical

chi-square values. The computed Likelihood Ratio (λ) = 5.11 was greater than the critical

χ2 = 0.01 for 2 degrees of freedom at 1 percent level of significance. Thus the null

hypothesis was rejected meaning that potato farmers were technically inefficient.

47

Table 4.7 Testing hypothesis on the presence of inefficiency in potato production Nyabihu District

Null hypothesis Parameters in the

hypothesis

Likelihood

Ratio (λ)

Critical

value

Decision

Inefficiency Model

δ i Coefficient of the

inefficient Model

Ho : γ =0

Ho: δ 1…= δ 8= 0

5.11

49.44

0.012

0.010

Reject

Ho

Reject

Ho

Source: Author’s presentation, 2010

Secondly, the null hypothesis determines whether the variables included in the

inefficiency effects model have no effect on the level of technical efficiency was tested.

The null hypothesis was rejected confirming that the joint effect of these variables on

technical inefficiency is statistically significant. (Ho: δ 1……… = δ 8= 0).

The calculated likelihood Ratio (λ) value was 49.44 while for 8 degrees of freedom at 1

percent χ2 value was 0.010. Given that the computed λ value was greater than the critical

χ2 value, the null hypothesis was rejected and concluded that there is influential technical

inefficiency caused by house hold size, education, gender, experience, marital status, firm

size, access to credit, and extension services.

48

4.2.3 Production frontier and Technical efficiency estimates

The maximum likelihood (MLE) estimates of the Cobb-Douglas model are presented in

Table 4.8. With an estimated gamma (γ ) value of 0.71, the study showed that about 71%

of the variation in the output of the respondents from the frontier was due to their

technical inefficiency. This indicates that farmers by far the largest portion of error

variation is due to the inefficiency error ui and not due to the random error vi implying

that the random component of the inefficiency effects does make a significant

contribution in the analysis. This means that technical inefficiency is likely to have an

important effect in explaining output among farmers in the sample. The one sided LR test

of γ = 0 provide a statistic of 5.11 which exceed the chi-square one percent critical value

of 0.01. The estimated ML coefficient showed that each of the inputs of potato firm size,

seed quantity, family labor and fertilize had positive values of 0 .18, 0.38, 0.42 and 0.12

respectively.

The Table 4.8 below shows almost that all these values are significant and have a positive

effect on Potato production. Therefore the increment of the variables such as, Area under

potato production, seed quantity, family labor, and fertilizer by one per cent will increase

output by 0 .18 , 0.38 , 0.42 , and 0 .12 per cent respectively except hired labor which

was not significant. The positive values imply that the present inputs used were not

optimal and yields would have increased from the additional use of inputs. Coelli et al

(1998) argues that stage I is inefficient because the addition of an extra unit of firm

should never produce. On the other hand negative values indicated that the input use has

reached the maximum level and more use of such input beyond the current level would

lead to reduced yields.

49

Table 4.8 Maximum likelihood estimates of the stochastic frontier production function

Variable Parameter Coefficient Std t - value error ________________________________________________________________________

Constant α0 4.08 *** (.660) (6.18 )

Area under potato (ha) α1 .18 *** (.073 ) ( 2.49 )

Seed quantity (Kg) α2 .389 *** (.062) (6.27)

Hired labor (Man day ) α3 .001 (.001) (0.1)

Family labor (Man day) α4 .42 *** (.200) (2.14)

Fertilize (Kg) α5 .12 ** (.081) ( 1.56)

Pesticide (Kg) α6 - .15 ** (.118) (- 1.27)

Sigma –squared, σ 2u +σ 2v σ 2 1.68

Gamma, σ 2u/σ 2 γ 0.71

Number of observations 123

Wald chi2(6) 681.4

Prob > chi2 0.000

Log likelihood - 189.64

Likelihood-ratio test of sigma=0:

Chi-square (01) 5.11

Legend: Asterisks indicate significance at the following levels: * 10% ; ** 5% , ***

1%

Source: Author’s presentation, 2010

50

However contrary to the expectation sign, the coefficient for pesticide showed a negative

value of 0.151, which was significant. The pesticide coefficient value was significant (P

= 0.013). This indicated that an increment of one percent of pesticide would reduce

output by 0.151 percent output.

Figure 4.3 indicated below shows the frequency distribution of technical efficiency

indices for the sampled Irish potato farms. The predicted technical efficiencies range

from a minimum of 22.8 percent to a maximum of 88.5 percent. The mean score

technical efficiency among smallholder potato farmers was 60.5 percent. The result

shows that it was possible for the farmers to improve their efficiency by about 39.5

percent.

Figure 4.3: The distribution of technical efficiency

0

5

10

15

20

25

30

35

20 -

30

31-

40

41-

50

51-

60

61-

70

71-8

0

81-

90

Efficiency score

Fre

quen

cy

Source: Author’s presentation,2010

51

4.2.4 Elasticities and Return to scale

Table 4.9 presents the results of elasticity values that henceforth indicate the relative

importance of every factor used in Irish potato production. The sum of the output

elasticities was 0.97. This value was less than one which implies the presence of

decreasing returns to scale (DRTS). According to Chavas et al. (2005) the presence of

DRTS in multi-input farm household models implies that the quantities of some inputs

exceed the scale efficient point. The results further revealed that family labor appears to

be the most important variable with elasticity of 0.42, followed by seed quantity. It

implies that increasing family labor use by 10 percent would lead to 4.2 percent increase

in output of potato production. This suggested that productivity would be higher if more

family labor is brought under Irish potato production.

Table 4. 9 Input Elasticity __________________________________________________________________

Variable Elasticity

__________________________________________________________________

Total firm size .182

Seed quantity .389

Hired labor .001

Family labor .428

Fertilize .127

Pesticide - .151

Decreasing Returns to scale (DRS) 0.976

Source: Author’s presentation, 2010

52

4.3. Factors influencing Technical efficiency Farmers’ socio-economic characteristics may influence farmers’ production decisions as

well as the overall technical efficiency in production. This section reports on sources of

inefficiency estimated in the model. A negative sign on parameter inefficiencies implies

that the variable reduces technical inefficiency while a positive sign increases technical

inefficiency. As expected the results in table 4.10 shows that, house hold size, gender,

marital status, experience, extension services, have a negative sign and therefore reduced

technical inefficiency (or increased technical efficiency) while education and firm size

have a positive sign which indicates increased inefficiency. The variables such as gender

and marital status were statistically significant at one percent while experience, house

hold size and extension services were significant at five and ten percent respectively.

Table 4.10 Determinants of technical inefficiency and Socio-economic Characteristics

Variable Parameters Coefficients Std t - error Value _____________________________________________________________________ Constant δ 0 11.59** .084 138.0 House hold size δ 1 -.163* .21 0.74 Education δ 2 .081 .21 3.69 Sex δ 3 -1.65*** .44 3.72 Marital status δ 4 -6.45*** 1.93 3.34 Experience δ 5 -1.34** .50 2.65 Farm size δ 6 .68*** .17 4.02 Access credit δ 7 -.08 .50 0.16 Extension services δ 8 -.69* .38 1.81 Lambda (u/v) λ 1.58

Sigma-squared (u) σ2 u 1.09

Sigma-squared (v) σ2 v 0.69

Source: Source: Field data Analysis Asterisks indicate significance at the following levels: * 10%, ** 5% , *** 1%

53

4.3.1 House hold size

Household size effects technical efficiency positively by 10 percent level of significance

indicating that larger households were more technical than the smaller ones. This maybe

attributed to the factors that these households consume more food and therefore strive to

achieve higher output. In addition these households have more labor available, which

may influence the supply of household labor for non-farm work (Bizoza et al, (2007).

4.3.2 Education level of household

According to Amos and Kibaara (2007, 2005) Education was expected to have significant

effects on technical efficiency. In many studies, education plays a significant role in skill

acquisition and technology transfer and farmers with higher levels of education were

likely to be more efficient in the use of inputs than their counterparts with little or no

education (Okoruwa et al, 2006). The results for the level of education of potato farmers

displayed in figure 6 shows that majority of the farmers did not complete secondary

education. Many of them did not go beyond primary school while the few who attempted

secondary education did not complete it. Similar study findings were obtained in Nigeria

by Idiong (2007). However in this study the level of education was positively and not

significantly related to technical inefficiency.

This implied that there was increased level of technical inefficiency as the level of

education increases. This was in contrast with the findings of Ferenji and Heidhues

(2007) and Raphael (2008) that education of the household had positive and significant

influence on the technical efficiency of farmers. This may be attributed to the orientation

of most farmers in the district where more than 60 percent did not complete primary

education.

54

4.3.3 Gender The coefficient of gender variable was negative (-1.65) at 1 percent level of significance.

This implies that gender of the household head was expected to have significant effects

on technical efficiency. Farms managed by men were expected to attain higher technical

efficiency than those that were managed by women. Nearly 80% of men were more likely

to have priority access to labor so that operations were done on time which increases

production efficiency in potato production. Males were more likely to deal with farming

operations that require much physical strength. It was therefore expected that a higher

value of this ratio leads to low technical efficiency. The same results on gender variable

shows male farmers to be more efficient. Kibaara (2005) found similar results among

maize smallholders in Kenya.

4.3.4 Farm size

The coefficient of farm size was positive and statistically significant at 1 percent level

indicating a direct relationship between farm size and technical efficiency. Land is

important in agricultural but is a limiting factor of production in Rwanda. Farm sizes

were very small averaging 0.83 hectares per household and getting smaller with

increasing rural population (Byiringiro 1996). Rwanda has a high rate of population

growth with individual’s limited access to land. When population pressure is high, land

subdivision is still going on leading to a fall in average farm size (Mpyisi et al., 2003).

4.3.5 Marital status

The estimated coefficient of the variable representing the marital status was positive and

significant at 1 percent. This implies that marital status was expected to have significant

55

effects on technical efficiency. The results obtained showed that 73.3 percent of the

respondents were married males involved in potato farming. The similar results were

found by Muhammad-Lawal et al (2009) in Ondo state, Nigeria .This could probably be

explained by the fact that the married males had access to the land because of cultural

prejudice and hence married men were closer to the frontier. In addition the married

males are heads of the household and had a responsibility to provide more food to the

family.

4.3.6 Experience of farmer growing potato The estimated coefficient for farming experience was negative and significant at 5

percent level showing direct relationship between farming experience and technical

efficiency. It indicates that efficiency increases with the number of years spent by the

household head in potato production. As they say, experience is the best teacher; this

suggests that the Irish potato farming in the study area was highly dependent on the

experience of farmers which may lead to better managerial skills being acquired over

time. This corroborates the findings by Amara et al (1998) and Khai et al (2008). This

result was also supported by Coelli ( 1996a) who concludes that old farmers are likely

to have more farming experience and hence less inefficient.

4.3.7 Extension services and access to credit

The coefficient for the variable of contact with access to extension services was

expected to have positive influence on technical efficiency of farmers. Similar results

were found by (Bagamba and Shuhao (2007, 2005) who indicates that extension services

being properly disseminated information to the farmers about better farming practices

56

and agricultural technologies to the farmers. This implies that extension plays a

significant role in improving technical efficiency in potato production. This result is in

line with the arguments by Nchare (2007) who indicates that regular contacts with extension

workers facilitates practical use of modern techniques and adoption of improved agronomic

production practices.

Furthermore the coefficient of access to credit variable was negative and statistically

insignificant. This implies that agricultural credit does not improve technical efficiency.

In the study area, access to credit was low with only 11.3% of the farmers able to access

credit (Table 4.5). However this study found no statistically significant relationship of

access to credit on technical efficiency. Similar findings were obtained in Malawi by

Tchale, et al (2007) who indicates that significant effect on credit access may reflect the

low levels of farmers’ access to credit among smallholder farmers. This is mainly due to

collateral requirements and high interest rates associated with seasonal agricultural loans

from the Malawi Rural Finance Company. However some farmers indicated willingness

to acquire credit but cited stringent requirement imposed by formal credit institutions

such as commercial banks and Agricultural finance corporations and the perceived risk

incase they default re-payment as the main constraints.

57

CHAPTER V

SUMMARY OF FINDINGS, CONCLUSIONS AND RECOMMENDATION S

5.1 Summary

In the study area, a sample of 150 agricultural farm households from three sectors of

Nyabihu district is drawn using stratified sampling technique. The cross-section primary

data for the study was collected by interviewing farm households through personal

interviewing technique.

Descriptive statistics was used to facilitate the characterization of smallholder farmers

who are involved in potato production. The survey results show a low literacy rate of

households with 35.5 percent attained only primary school and 56.9 percent did not

complete primary education but most of the farmers are experienced with more than 12

years farming experience. The results obtained showed that there are more males

involved in potato farming than females. The majority of farmers, 67 per cent, have

landholding between 1-1.5ha and 22.7 per cent have land holding between 0-0.9 ha.

Moreover the study employed the stochastic production frontier approach to estimate

technical efficiency in potato production. In the stochastic production frontier model,

maximum likelihood was estimated and indicated that each inputs such as, area under

potato, seed quantity, family labor, and fertilize had a significant positive effect on

potato productivity. In the technical inefficiency model it was found out that house hold

size, gender, marital status, experience, extension services, positively and significantly

influenced technical efficiency of smallholder potato farms in Nyabihu district.

58

The results obtained from the stochastic frontier estimation indicate that the mean score

technical efficiency of farmers given was 60.5 percent while the maximum is 88.5

percent. This indicates that there is a scope of further increment of output growers by

39.5 percent without increasing the levels of inputs used. The sum of the output elasticity

is 0.976 which indicates decreasing returns to scale (DRTS) implying that farmers lose

efficiency if they increase scale of production. Furthermore the gamma (γ ) value was

0.71 indicating that 71 percent variation in the output of Irish potato production was

attributed to technical inefficiency.

5.2 .Conclusion The purpose of this study was to examine the technical efficiency of smallholder potato

production and determine factors influencing technical inefficiencies in Nyabihu District-

Northwestern Rwanda. The results of the study revealed that technical efficiency for

smallholder Irish potato growers was low which suggested the presence of technical

inefficiency. However maximum likelihood estimates indicated the coefficients for

area under potato production, seed quantity, family labor, and fertilize are positive and

significant. The coefficient on pesticide is negative but insignificant implying that both

inputs are possibly being under utilized. The contribution of the family labor and seed

quatity in increasing production are more pertinent.

The concerted efforts from both political and technical considerations are highly needed

to mitigate challenges which are affecting the progress of food crop. Notably, there is

urgent need to improve the knowledge of farmers on effective use of inputs and enhance

a favorable credit system which meets social and economic conditions of small farmers in

order to increase their purchasing power to enable them buy agricultural inputs.

59

The study also identified that extension services were doing well in the study area. Given

the large coefficient estimate on extension services in Table-4.10, improvement in these

services can play a significant role in improving technical efficiency in potato production.

For all these to take place, it is high time that agriculture sector receive due attention and

input from the government so as to advance the country’s objectives of growth and

poverty reduction.

5.3 Recommendation The study recommends accessibility to credit facilities to enable farmers acquire

agricultural inputs hence improving technical efficiency. Findings of the study have

important policy implications, the positive effect of access to extension services implies

that enhancing smallholder farmers’ access to information and new technologies will

improve the level of efficiency. The study recommends that policy makers should focus

on innovative institutional arrangements to enhance extension and farmers’ training such

as use of group approach, farmer-led extension e.g. farmer field schools and

strengthening mass media to supplement and complement extension workers efforts

besides extensive use of information and communications technology (ICT) to support

agricultural extension.

Secondly, another area for policy focus is on strategies for integrating women into the

training and extension programs which may also help to increase efficiency in the

research area. As far as the problem of farm size and rapidly increasing population

density in Rwanda is concerned , technical efficiency of farmers could increase their

income through proper application of fertilizers, use of family labor and consolidation of

60

small holder farms by forming farmer’s co-operatives and establishment of policies

aimed at reducing household size.

This study further recommends the government to educate inexperienced farmers through

proper agriculture extension services that could have a great impact on increased level of

efficiency and hence agricultural productivity.

5.4. Suggestions for Further Research This study only focused on the technical efficiency of the Irish potato farm fields in

Nyabihu district. It would be useful to focus future research on the economic evaluation

of extension services by estimating the costs versus benefits of these services which will

enable policymakers to design appropriate agricultural policies with regard to the future

role of extension services.

For over decades, the governments and research organizations have largely focused on

increasing productivity of food crops as a measure to achieve rural sustainable

development hence one of the strategy to achieve the millennium development goal

(MDG) of food security.

61

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70

APPENDIX

1. Maximum likelihood estimates for parameters of the stochastic frontier (translog)

and Inefficiency model for smallholders potato production.

Variable

Parameters Coefficient Standard Error

t- ration

________________________________________________________________________ Frontier Model Constant β 0 18.14 5.95 3.05 Ln( total firm size) β 1 -2.71* 1.15 -2.35

Ln ( Seed quantity) β 2 1.92* .79 2.41

Ln (hired labor) β 3 -.030* .014 -2.15

Ln (family labor) β 4 -1.30 * 2.20 -0.59

Ln (fertilize) β 5 -2.18 * 1.02 -2.13 Ln (pesticide) β 6 -.67 ** 1.33 -0.51

Ln( total firm size)2 β 7 .130 .14 0.89

Ln ( Seed quantity)2 β 8 .02 .04 0.55

Ln (hired labor)2 β 9 -.00 .00 -1.09

Ln (family labor)2 β 10 .00 .00 .00

Ln (fertilizer)2 β 11 -.008 .23 -0.04

Ln (pesticide)2 β 12 -.05 .35 -0.15

Ln total firm size * Ln Seed quantity β 13 -.04 .07 -0.56

Ln total firm size * Ln hired labor β 14 .003 * .001 2.48

Ln total firm size * Ln family labor β 15 .29 .16 1.77

Ln total firm size * Ln fertilize β 16 .21 .11 1.86

Ln total firm size * Ln pesticide β 17 .78 .24 3.23

Ln Seed quantity* Ln hired labor β 18 -.00 .00 -0.01

Ln Seed quantity* Ln family labor β 19 -.75** .31 -2.36

Ln Seed quantity* Ln fertilizer β 20 .044 .14 0.30

71

Ln Seed quantity* Ln pesticide β 21 -.32 .18 -1.76

Ln hired labor * Ln family labor β 22 -.003 .003 -0.96

Ln hired labor * Ln fertilizer β 23 -.001 .001 -0.84

Ln hired labor* Ln pesticide β 24 .001 .002 0.68

Ln fertilize * Ln pesticide β 25 .014 .15 0.10

Ln fertilize * Ln family labor β 26 .10 .19 0.54

Ln pesticide *Ln family labor β 27 -.22 .37 -0.62

Inefficient Model Constant δ 0 -.42 3.92 -0.11

House hold size δ 1 -2.51 * .61 -4.12

Education δ 2 -1.29 * .57 -2.24

Sex δ 3 -3.09 1.81 -1.71

Marital status δ 4 -5.59 * 1.87 -2.99

Experience δ 5 3.78 ** 1.26 2.98

Farm size δ 6 1.78 .61 2.91

Access credit δ 7 -1.08 .98 -1.10

Extension services δ 8 3.73 * 1.17 3.17

Lambda (u/v) λ 1.33 .28 4.71

Sigma-squared (u) σ2 u 0.71 0.04 17.0

Sigma-squared (v) σ2 v 1.24 0.07 17.0

Number of observations 123

Wald chi2(26) 212.27

Prob > chi2 0.0000

Log likelihood -192.18019

Likelihood-ratio test of sigma=0:

Chi-square (01)

2.42

Legend: Asterisks indicate significance at the following levels: * 1% ; ** 5% ,

72

Appendix 2. Testing of Multicollinearity using correlation coefficient Area under

potato prod

1.00

Seed quantity 0.51 1.00

Family labor 0.12 0.05 1.00

Fertilizer 0.13 0.1196 0.15 1.00

Hired labor 0.17 0.22 0.02 0.13 0.03 1.00

Source: Author’s Analysis

73

2. QUESTIONNAIRE FOR POTATO PRODUCERS

The purpose of this study is to evaluate the Technical efficiency of Irish potato production in

Nyabihu District.

Please note that your responses will remain confidential.

-------------------------------------------------------------------------------------

A. HOUSEHOLD SURVEY QUESTIONNAIRE

A. SURVEY QUALITY CONTROL

QUESTIONNAIRE NUMBER

__________________________________________

NAME OF ENUMERATOR

____________________________________________________________________

SECTOR

_____________________________ FAMILY NAME OF RESPONDENT

________________________________________________________

CELL

______________________________VILLAGE ( UMUDUGUDU)

CHECKED BY __________________________________DAY

___________MONTH_________

DATE OF INTERVIEW: DAY_________ MONTH

____________

ENTERED BY ______________________________________DAY

___________MONTH_________

DURATION OF INTERVIEW (MINUTES) MIN

1A . Number of persons in the household -------------------------------------------------------------------

74

B. CHARACTERISTICS OF HOUSEHOL

2. What are the main problems that you experience in

Potato production?

Name of household B2A.

sex

1. Male

2.Famale

B3A.

Age

(years)

B4A.

Marital Status

Single=1

Married =2

Divorced/separate

d =3

B5A.

Education level

Never went to school=1

Not finished primary

school =2

Finished primary

school = 3

Professional school = 4

Not finished primary

school =5 Finished

secondary school=6

Not Finished

university=7

Finished university=8

B6A.

For how long

have you been

growing

potato

One year =1

Five years =2

Ten Years =3

More ten

years = 4

75

3. C. LAND

C1A . What is the total size of your farm?

acre =1

half of hectare =2

Hectare = 3

More than hectare = 4

Less than acre =5

-------------------------

C2B Is it your own land : Yes =1 No =2 ----------------

C2C If is yes :

Is it inherited=1 --------------

You Purchased it =2

1&2 = 3

C2D Is it your rented =1

-------------

Is it your borrowed =2

1&2= 3

76

4. D LABOUR USE IN POTATO

D 1A . LABOUR USE IN POTATO

Activity D1A. Land preparation

D1B. Planting

D1C. Weeding

D1D. Fertilizer/ manure application

D1E. Harvesting

D1F. Transportation

D1G .others

Did use the Family labour Yes= 1 No =2

How many

hours – days

How many

person-days

The price

person –day

The total

labour cost

5. E. Do you belong to any to the Association, Cooperative of Potato production? Yes= 1 No = 2 E1A Which position do you have in the cooperative? Chairman =1 Secretary =2 Member only =3

---------------

E2B How the cooperative help you in potato production?

6 . F. POTATO PRODUCTION

F1A. What was the yield

(in kilograms) from last 2

season’s crop?

F2B.size of

Farm

F3C. Seed

used

F4D. Production

(Kgs)

F5D.Price( Kg) F6E.

Total

77

7. G INPUT USE IN POTATO

Did you use inputs (fertilizers, manure, pesticides, others) in your potato last seasons?

Yes/No………………

8. H . SEED USE IN POTATO

H1A What variety(ies) of potato did you grow last

season?

H3A.Which seed did you grow last year? ..................

H4A How many kilograms of seed did you plant?

-------------------------Kg

Improved =1

Local =2 -----------------

---

Names of Fertilizer

Code G1A. Quantity? G1B

Measurement

Kilo=1

Litter= 2

G1C. Price kg G1D. Total

a.Fertilizer

NPK=1

DAP=2

Urée= 3

b. Manure

Imborera =1

Amase =2

Amatungo magufi

=3

Ikimoteri =4

c. Pesticide

Dithane =1

Ridomir=2

Thiodan=3

f. other (specify)

78

H2A Where did you get the seed that you planted

from?

Own =1

Neighbor =2 --------------

-----

Government assistance =3

other= 4

H5A. Did you apply fertilizers on the plot of potato last season?

Yes=1 ------------

No=2

H6A If Yes , how many ?...........................................Kgs.

9.I. PRODUCTION OF LIVESTOCK KEPT

Type I1A. Number Kept

I2A. Number of cows milk kept

I3A.How many days did you milk your cow

I4A.How much liters do you get /days Litres/day

I5A. Which animals assist you to increase fertilizers(manure)

I6A. Production (specify product and units) Meat = 1 Eggs =2

I7A.Price of liter of milk Egg =kilo Meat=kilo

I8A.

Total

Cow=1

Goat=2

Sheep=3

Pig=4

rabbit=5

Poultry

= 6

10. J. LABOUR USE IN LIVESTOCK

Type G1A. Activity G2A. Do you use family

labor .

Yes = 1 -------------

No = 2

G6A If , Yes, How much

Person –day

G3A. Do you pay your lobar

monthly? How many hours – days

79

1. Cow Feeding

Milking

Tick control

Deworming

Others (specify)

2. Poultry Feeding

11. K. ACCESS TO CREDIT

K1A Do you access credit to enhance Potato production? (1) Yes…... (2) No……

K2 A If yes, Please fill the table below:

K2B Source of

credit

K2C

Amount

K2D

Repayment

period

K2C.Interest

rate

K2D. Did the credit

assist you to grow the

potato?

K2E. How did you

utilize it?

K2F If no, why not:

The banks and Micro finance institutions are far = 1

What the requirement to access to the credit? =2

The rate of interest rate is high.=3

Other =4

80

12. L. EXTENSION SERVICES

L1A Do you receive extension officer visit you about

potato production last season?

Yes = 1

No= 2 ------------------

K2A If Yes , How many times in a month 1)Once a month ------------------------

2) 3 times a month ----------------------

3)Once in 6 months ----------------------------

4) Not at all

29. If visited, what message did they carry?

Message ------------------------------------------

K4A. If None, How do you acquire extension

information?